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ROBUSTLY SHADOWABLE CHAIN COMPONENTS OF C1 VECTOR FIELDS
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 Title & Authors
ROBUSTLY SHADOWABLE CHAIN COMPONENTS OF C1 VECTOR FIELDS
Lee, Keonhee; Le, Huy Tien; Wen, Xiao;
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 Abstract
Let be a hyperbolic closed orbit of a vector field X on a compact boundaryless Riemannian manifold M, and let be the chain component of X which contains . We say that is robustly shadowable if there is a neighborhood of X such that for any , is shadowable for , where denotes the continuation of with respect to Y. In this paper, we prove that any robustly shadowable chain component does not contain a hyperbolic singularity, and it is hyperbolic if has no non-hyperbolic singularity.
 Keywords
chain component;dominated splitting;homoclinic class;hyperbolicity;robust shadowability;uniform hyperbolicity;vector field;
 Language
English
 Cited by
1.
SHADOWABLE CHAIN COMPONENTS AND HYPERBOLICITY,;;;

대한수학회보, 2015. vol.52. 1, pp.149-157 crossref(new window)
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Weak measure expansive flows, Journal of Differential Equations, 2016, 260, 2, 1078  crossref(new windwow)
2.
HYPERBOLICITY OF HOMOCLINIC CLASSES OF VECTOR FIELDS, Journal of the Australian Mathematical Society, 2015, 98, 03, 375  crossref(new windwow)
3.
SHADOWABLE CHAIN COMPONENTS AND HYPERBOLICITY, Bulletin of the Korean Mathematical Society, 2015, 52, 1, 149  crossref(new windwow)
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